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Nonzero Symmetry Classes of Smallest Dimension
Published online by Cambridge University Press: 20 November 2018
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Let U be a k-dimensional vector space over the complex numbers. Let ⊗m U denote the mth tensor power of U where m ≧ 2. For each permutation σ in the symmetric group Sm, there exists a linear mapping P(σ) on ⊗mU such that
for all x1, …, xm in U.
Let G be a subgroup of Sm and λ an irreducible (complex) character on G. The symmetrizer
is a projection of ⊗ mU. Its range is denoted by Uλm(G) or simply Uλ(G) and is called the symmetry class of tensors corresponding to G and λ.
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- Copyright © Canadian Mathematical Society 1980
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